A direct integral pseudospectral method for solving a class of infinite-horizon optimal control problems using Gegenbauer polynomials and certain parametric maps

<abstract><p>We present a novel direct integral pseudospectral (PS) method (a IPS method) for solving class of continuous-time infinite-horizon optimal control problems (IHOCs). The transforms the IHOCs into finite-horizon in their forms by means certain parametric mappings, which are then approximated finite-dimensional nonlinear programming (NLPs) through rational collocations based on Gegenbauer polynomials and Gegenbauer-Gauss-Radau (GGR) points. paper also analyzes interplay between maps, barycentric GGR points convergence properties collocated solutions IHOCs. Some formulas construction interpolation weights GGR-based integration differentiation matrices barycentric-trigonometric derived. A rigorous study error proposed is presented. stability analysis Lebesgue constant investigated. Two easy-to-implement pseudocodes computational algorithms computing described. Three illustrative test examples presented to support theoretical results. We show that collocation leveraged with fast accurate NLP solver converges exponentially near-optimal approximations coarse mesh grid size. shows typical spectral/PS methods classical Jacobi maps usually diverge as number grow large if computations carried out using floating-point arithmetic discretizations use single grid, regardless whether they Gauss/Gauss-Radau type or equally spaced.</p></abstract>